Because the likelihood of protests turning violent and damaging property is high? I really don't see how we can say that protesting is a "protected activity" and yet not allow people to have an actual say in how things should be run. Almost as if we want people to think they can have a say (by protesting - yay, it's "protected"!), but not really give them an avenue to do so that is meaningful and likely to change things, except for physically showing up in concerted numbers to prove their opinion?
From my perspective, protests appear to just be there to amplify loud minority opinions and distort the discussion at this point. For all we know, we're hearing the vocal minority of people, instead of the actual voices that need hearing.
If we really wanted to fix protesting, to take an example: Homosexual discrimination at the workplace. Have a platform or "offline vote" if you will where all homosexual individuals are asked to rate their work experience, whether they had been discriminated against and what action they think should be taken, with the assumption that if it's found, that action needs to be taken. They then "vote", and we see the results.
I bet that if the majority saw the results, they'd rightfully make their mind up pretty quickly. Instead, we forced homosexual individuals for years/decades to protest and complain about the things that were rightfully affecting them, and only once it reached some arbitrary critical mass, we as the rest of society decided to change. What were we "waiting" for exactly? For people to change their minds? People to cave in after being worn down even though they don't agree? Societal opinions to shift? A new generation grown up with the movement being taught to them by elementary school teachers? Cultural norms to adapt?
Also, if we did get there and such a vote isn't followed up by actual action, then maybe our system of government is broken and we should fix it. Perhaps for that we should go out and protest.